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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 16, NO. 12, DECEMBER 2006 1507

Robustness Enhancement for NoncentricQuantization-Based Image Watermarking

Soo-Chang Pei, Fellow, IEEE, and Jun-Horng Chen, Member, IEEE

Abstract—This paper presents a novel approach for improvingthe robustness of the quantization-based watermarking scheme.Unlike the conventional approach, which quantizes the host valueto the center of the objective interval, the proposed scheme offersthe flexibility of determining the quantized value. Given tolerableembedding-induced distortion and the host value, the quantizedvalue can be analytically determined in a closed-form solution, in-stead of being fixed at the center of the interval. To objectively com-pare the robustness, different watermarking schemes are imple-mented in the same distortion-to-noise ratio (DNR) scenario andthen the probabilities of error detection are measured. Simulationresults indicate that the proposed scheme, compared to the conven-tional quantization watermarking, could reduce the error proba-bility by 0.113 when DNR is set to 0 dB, whereas the reductionis only 0.037 for the recent Wu’s approach. Furthermore, withoutthe finite possible values of the watermarked data, the proposedscheme provides sufficient nondisclosure for the quantization step,whereas in the conventional quantization-based watermarking, thequantization step can be easily inferred from the watermarkeddata.

Index Terms—Blind detection, DNR, informed detection, quan-tization-based watermarking, robustness.

I. INTRODUCTION

FOR various applications [1], the image watermarkingsystem is developed to embed additional information

into the host image. The embedded message may carry theownership or secret information. Conventional cryptographicsystems only allow holder of a valid key to access the encrypteddata. However, the decrypted data became untrackable, and thecopyright protection thus becomes invalid. A watermarkingsystem can be considered a complement of the cryptographicsystem. Especially, the watermarked image is visually identicalto the host image.

Fig. 1 illustrates a generic diagram of a watermarking system.The host signal is modified to become the watermarked signal

to convey the watermark message . Generally, the water-marked signal inevitably suffers the channel effect, which mayresult from malicious attacks or unintentional processes. How-ever, the extracted watermark is expected to be as close toas possible. The scrambling and descrambling processes can

Manuscript received Ocotober 17, 2004; revised May 9, 2006. This work wassupported in part by the National Science Council, Taiwan, R.O.C., under Con-tracts NSC 94-2213-E-002-072 and NSC 93-2752-E-002-006-PAE. This paperwas recommended by Associate Editor E. Izquierdo.

S.-C. Pei is with the Department of Electrical Engineering, National TaiwanUniversity, Taipei 106, Taiwan, R.O.C. (e-mail: [email protected]).

J.-H. Chen is with the Department of Communication Engineering, OrientalInstitute of Technology, Taipei 220, Taiwan, R.O.C. (e-mail: [email protected]).

Digital Object Identifier 10.1109/TCSVT.2006.885174

Fig. 1. Schematic diagram of a watermarking system.

provide three functions of the watermarking system: security,cropping-resisting [2], and message shaping [3].

Security: The scrambling and descrambling processes aregenerally controlled by a random seed which can be re-garded as a secret key. Only those who hold the key canview the watermark message.Cropping-resisting: If the watermark is a bilevel andvisually recognizable image (like a seal, emblem, etc), thetwo-dimensional random permutation of the watermarkimage will disturb its spatial relation, preventing piratesfrom easily removing the watermark message by cropping.Message shaping: The distribution of the binary water-mark message is generally assumed to be equally probable,

. This is intended to re-move the influence of message distribution. Therefore, viaan exclusive OR process with a random message , where

, the distribution of thewatermark message is guaranteed to be equally probable.

Actually, in the above functions, the receiver only requires therandom seed, which is usually not too long, to use as the se-cret key to reveal the watermark message. In [4], the securityrequirement is achieved by sending a secret key with the samelength as the watermark message. However, the watermarkingscheme becomes impractical when too much overhead informa-tion is involved.

For invisible watermarking, the embedding should not benoticeable when constricting the extent of the superimposeddistortion. Meanwhile, the watermarked image is subject tothe channel effect, which may cause the wiping off of the em-bedded message. Accordingly, the embedded message shouldbe sufficiently robust to survive reasonable1 attacks on the

1Generally, an applicable watermarking scheme ensures that the severe degra-dation of fidelity of the watermarked image follows the attack which makes theembedded message be irretrievable. Namely, the attacks, which seriously de-teriorate the visual quality of the watermarked image, are excluded from thediscussion of the watermarking scheme.

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1508 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, VOL. 16, NO. 12, DECEMBER 2006

watermarked image. Generally, the embedded signal with ahigher energy strength makes the watermarked image morecapable of withstanding attack, yet induces more perceptualdegradation. Therefore, the designers of watermarking systemusually face the dilemma of robustness and transparency.

Additionally, the quantity of embedded information (namelythe capacity), which determines the ability to distinguish dif-ferent messages (or different proprietors), is also a fundamentalproblem of watermarking schemes. Usually, capacity is mea-sured based on the number of bits which can be embedded in ahost sample (bits per sample). How many bits of the embeddedmessage are satisfactory depends on the application the water-marking scheme is applied to. In the application of access con-trol, capacity demand is not so much [5]. However, the appli-cations of fingerprinting and information-hiding may demandhigh payloads of the embedded information. Recently, manyresearches of the digital rights management (DRM) addressedthe issue of benchmark of the watermarking system in mul-tidimensional criteria evaluation. The optimization of the wa-termark parameters (robustness, transparency, and capacity) ismutually competitive and cannot be clearly done at the sametime [6]. A reasonable method of comparing different water-mark schemes involves measuring the error probabilities of themessages extracted from the watermarked images with the sameDNR,2 where the watermarked images contain equal quantityof information. Naturally, unlimited embedding-induced distor-tion can not be allowed in practical applications. The measure-ment and comparison in this work consider the watermarkedimage should be indistinguishable from the host image.

Cox et al. [7] proposed a simple and extensively used scheme,spread spectrum (SS), which purely adds a watermark signal

to the host signal

(1)

where denotes a scalar function of embedded message, and represents a pseudo-random spreading vector. In [7],

the host signal is a vector in the frequency domain of thehost image. If the host signal is known to the receiver (i.e.,informed detection [8]), the embedded message can be easilyand accurately estimated from the attacked watermarked signal

, because the host-interference is removed and thewatermark signal is uncorrelated with the additive noise

. However, in some applications, the host signal is unlikelyto be available at the receiver (blind detection). Malvar et al.[9] thus proposed the improved spread spectrum (ISS), whichmodulates the energy of the inserted watermark to compensatefor the host-interference. This scheme modifies (1) as

(2)

A simpler version of is a linear function, that is,. However, the later section demonstrates

2the ratio of the embedding-induced distortion and the power of the attackinginduced noise.

that the ISS is beneficial only for high embedding-induced dis-tortion or low capacity.

Chen and Wornell [10] proposed quantization index modu-lation (QIM) which has been demonstrated to be an effectivemethod for digital watermarking because it could blindly esti-mate the embedded message with almost the same accuracy asthe accuracy of the host image being available at the receiver.Especially, spread-transform dither modulation (STDM) is alow-complexity realization, in which the projection of the hostsignal along a pseudo-random vector is quantized to the centerof the nearest interval referring to the embedded message. Gen-erally, the quantization intervals are nonoverlapping and all havethe same size. Thus, all of the quantized values are equally sep-arated in the range of the possible values and are alternately as-signed to messages “1” and “0.” To enhance the security pro-tection, Wu [11] recently proposed that the look-up table (LUT)should be built on top of a general quantization-based water-marking, in which the quantization intervals are randomly as-signed to “1” or “0,” with the constraint that the runs of “1” and“0” have limited length. However, the approach developed byWu can only improve the robustness of QIM in the low DNRcase, where the probability of error detection is usually high.

Many adaptive watermarking methods were proposed foroptimizing the performances of robustness and transparencysimultaneously. Barni et al. [12] relied on some of the ideasexposed in [7] and exploited the spatial masking characteristicsof the HVS to enhance the transparency property. The strengthof the watermark embedding is modulated according to thelocal spatial statistics. For the highly textured regions, whichare characterized by low-noise sensitivity, the watermark canbe embedded to a mighty extent, whereas in the uniform re-gions, which are more sensitive to change, the watermark isembedded only to a minor extent. Different from the generalwavelet-based watermarking, Bao and Ma [13] applied theQIM [10] approach on singular values of the wavelet domainfor image authentication. On the basis of the idea that slightvariations of singular values do not affect the visual perceptionof the image, the watermark bits are embedded on the singularvalues for each of the wavelet domain blocks, with the quan-tization steps adaptive to the statistical model of the blocks.Chang et al. [14] adopted the fuzzy adaptive resonance theory(Fuzzy-ART) classification to identify appropriate DCT blocksfor watermarking. The embedding strength is determined bythe intensities of the high and low frequency components in theselected blocks. Stronger embedding strength is used in thoseblocks with fewer large magnitude DCT coefficients and viceversa.

Following the conventional quantization technique, whichminimizes the quantization error to satisfy the needs of codingor compression, most of the quantization-based watermarkingschemes quantize the host value to the center of the objectiveinterval. This work proposed that the quantized value is nolonger located at the center of the quantization interval, butrather is determined by the host value and the embeddedmessage. This flexibility of the quantized value diminishesthe embedding-induced distortion, and can coordinate thetransparency and robustness requirements of a watermarking


PEI AND CHEN: ROBUSTNESS ENHANCEMENT FOR IMAGE WATERMARKING 1509

Fig. 2. Conventional quantization-based watermarking.

scheme. Experimental results demonstrates that the proposedscheme effectively improves the robustness performance ofother quantization-based watermarking schemes.

Once the robustness is improved, the watermarking approachcan be more extensively applied to various scenarios. Especiallyin the applications of data hiding, lower error rate implies widertransmission bandwidth and more amount of conveyable infor-mation. For example in video watermarking, watermark annota-tion makes the host data convey side information for achievingadditional functionalities, automatic monitors of the broadcastdata, and device control, etc.

II. QUANTIZATION-BASED WATERMARKING

The quantization-based watermarking scheme is discussedhere to demonstrate the performance improvement of the pro-posed scheme. The quantization-based watermarking schemesare shown to be able to extract the embedded message withoutrequiring the host signal. Additionally, although the spreadspectrum (SS) [7] based watermarking is proposed to be suit-able for informed detection, Malvar et al. [9] declared thatblind detection can also be applicable to the ISS watermarkingscheme. Therefore, this section also presents the performanceanalyses of SS and ISS in order to compare them with theproposed scheme in the following sections.

A. Conventional Quantization-Based Watermarking

Fig. 2 illustrates the main concept of the quantization-basedwatermarking. The embedding domain is divided into subsetswith quantization step , and the subsets are alternately des-ignated as “interval-0”. Let denote the host value and

represent the one-bit message to be embedded, then theembedding is denoted as

(3)

where is a uniform quantizer with step size , anddenotes a message modulating function mapping the embeddedmessage to .

Inheriting from the quantization techniques applied to com-pressing or coding, which attempt to minimize the quantizationerror, the quantization in (3) chooses the center of the intervalas the quantized value. However, the quantization-based water-marking should additionally consider the message to be em-bedded. As shown in Fig. 2, both and are the centers ofthe corresponding intervals. In the embedding process, the hostvalue is replaced by when is located in the interval whichrepresents the same message as that to be embedded; and ischosen as the quantized value in the opposite case. If the above

two cases occur with equal probability, the embedding-induceddistortion, measured by mean squared error (MSE), is

(4)

where denotes the density function of in the region of0 to . Assuming is uniformly distributed over the region,3

the distortion is expressed by

(5)

Regarding the extracting process, the receiver simply deter-mines the embedded message according to the interval in whichthe received value is located. Notably, the receiver does not re-quire the host signal. However, the channel noise , which mayresult from malicious attacks or unintentional signal processes,can contaminate the watermarked signal such that the receivedsignal is . The extracted message bit is correct pro-vided and are located in the intervals which represent thesame message. Namely, the detection error will occur when thestrength of the attack noise is in the following range:

Therefore, the error probability of detection is

(6)

where denotes the density function of the noise . Theapproximation of (6) is only valid when is symmetricaland unimodal.4 If the noise is the Gaussian distribution withzero mean and variance , (6) becomes

(7)

3The host value x is not always uniformly distributed. However, if the quan-tization step q is sufficiently small, the distribution of x can be approximatelyconsidered uniform.

4Certainly, the mode of the density function will be zero. Besides, the rate ofincrease below the mode and the rate of decrease above the mode should be asfast as possible, otherwise the approximation will yield considerable inaccuracy.



where the complementary error function is defined as

Clearly, (6) and (7) are influenced by quantization step . Es-pecially in (7), larger value of reduces the error probability,yet increases the embedding-induced distortion. Therefore, theDNR is generally defined as

(8)

Thus, the probability of error detection can be represented interms of

(9)

Though (9) fairly describes the robustness performance, the em-bedding-induced distortion is not unlimited. After all, the wa-termarking is in vain if the transparency requirement can not beachieved.

Chen and Wornell [10] named the embedding technique pre-sented in (3) dither modulation (DM), which is derived fromdither quantization [15]. The dither quantization attempts toobtain a higher reproduction quality from the quantized signalthan the general quantization. However, the dither signal usedin dither quantization is a random signal, yet is a deterministicsignal determined by the embedded message in watermarking.The DM approach also appears to resemble the so-called least-significant-bit(s) (LSB) [16] coding or low-bit(s) modulation(LBM), but in reality does not. The LSB coding or LBM be-gins by setting the least-significant-bit(s) of the host value tozero. One of two values, represented as “1” and “0,” is addedto according to the value of the embedded message. Thesetwo representative values are usually the minimum and max-imum of the range of the least-significant-bit(s). Fig. 3 showsthe input-output ( versus ) characteristic functions of DMand LBM coding, respectively. Since the quantized values for

and in Fig. 3(a) and (b) are all separated by adistance of , they have the same abilities to withstand the noiseattack. Nevertheless, the DM and LBM coding approaches paydifferent costs of embedding-induced distortion. In Fig. 3, thearea enclosed between the characteristic function and the 45line indicates the absolute distortion, , resulting from theembedding process. Observing the range for to , theaverage area for embedding message and is byDM, and by LBM coding. That is, to achieve the same ro-bustness performance, the DM approach pays less cost in terms

Fig. 3. Input-output characteristic functions of (a) dither modulation and(b) LBM coding. The solid line is form = 1 and the dashed line is form = 0.

of embedding-induced distortion than LBM coding. The MSEof the LBM coding can also be calculated by

(10)

Comparing (5) and (10), the LBM coding induces 1.75 timesmore MSE than the DM approach.

To alleviate the embedding-induced distortion superimposedon one sample of the host signal, the host signal can be parti-tioned as the -dimensional vectors , each vector is then trans-formed to a scalar which is the embedding object. The embed-ding domain comprises all possible values of . Consequently,the capacity of the watermarked signal is bits per sample.By embedding the message into transformed value , the distor-tion is spread over each dimension of . For example, in [10], theauthors projected the host vectors along randomly determineddirections and quantized the projection values, and named thismethod spread transform dither modulation (STDM). Besides,the randomness of the directions to be projected on can provide asecret communication between the embedder and the extractor.In STDM, the embedding-induced distortion is of (5)

(11)

The host signal is not always partitioned into vectors to reducethe distortion on one sample. In [11], the author traded robust-ness for the visual quality of the watermarked image. Regardingthe increase in error probability, each bit of the watermark mes-sage was embedded repetitively. Using the repetition codingmethod can reduce the overall probability of detection error.STDM and repetition coding are compared in Section II-B.

In the conventional quantization-based watermarking, thepartitioned intervals are alternately designated “interval-1” and“interval-0.” In [11], the author recently introduced a LUT ap-proach instead of following this convention. A predefined table,which randomly maps the quantization intervals to message



bits “1” or “0,” enhances security of the watermarking system.Compared to the conventional quantization-based water-marking for the same quantization step size, the LUT approachresults in more embedding induced distortion and less errorprobability. However, the author of [11] demonstrated that theLUT approach outperforms conventional quantization-basedwatermarking in robustness in the same DNR scenario. If runsof “1” and “0” are limited to a length of two, then the overallembedding-induced distortion is shown to be [11]

(12)

and the probability of error detection under the Gaussian noisethen can be approximated by

(13)

Actually, the LUT approach only achieves an improvement inthe case of low DNR. Undoubtedly, the error probability in-creases as the DNR decreases. That is, under stringent detectionaccuracy requirements, the application of the LUT approach isconfined to the cases of low capacity. This study shows thatthe proposed scheme outperforms the other quantization-basedwatermarking schemes in most of the applicable scenarios, andhence raises the feasibility of embedding the information withhigh capacity.

B. Spread Transform Versus Repetition Coding

As discussed in Section II-A, either spread transform orrepetition coding can be used to trade capacity for reducingembedding-induced distortion. This investigation comparesthe contributions of these two approaches to the quantiza-tion-based watermarking schemes. The comparison is based onthe premise that two approaches are applied to embed the sameamount of information, and the probability of error detectionfor the case of the same DNR is then presented, where theattack noise is Gaussian. This investigation assumes that, inthe spread transform approach, the host signal is partitionedinto -dimensional vectors, each vector conveys one-bit of themessage, and the same message bit is repeatedly embeddedinto samples of the host signal in the repetition coding.

From (7), (8), and (11), the probability of error detection forthe spread transform is

(14)

For repetition coding, the decoding process should incorporatethe majority voting. That is, the overall probability of detectionerror will be

(15)

Fig. 4. Comparison of the contributions to quantization-based watermarkingfor spread transform and repetition coding.

where

To avoid the ambiguity associated with majority voting, is setto an odd number ranging from 1 to 255. Regarding the settingof DNR, a practical condition is considered below.

The peak signal-to-noise ratio (PSNR) is most commonlyadopted to assess the image quality, and is defined as

(16)

where denotes the MSE superimposed on one sample. More-over, let and represent the PSNRs of the wa-termarked and the attacked watermarked images, respectively.The corresponding DNR can be determined as

(17)

For example, the DNR is set to 3.35 dB to reflect the situationwhere the PSNR of the watermarked and the attacked water-marked images are 40 and 35 dB, respectively.

Fig. 4 illustrates the analytical results of (14) and (15), andthe experimental results for 1 000 000 randomly generated sam-ples, with the DNR set to 3. The simulation results are clearlyconsistent with the analytical results. Both the spread transformand repetition coding can lower the detection error by embed-ding less information. Furthermore, the spread transform offersa greater contribution to the improvement of robustness thanrepetition coding.



C. Spread Spectrum (SS) Watermarking

The original spread spectrum watermarking [7], unlike thequantization-based watermarking, is difficult to be applied tocases involving blind detection. In the quantization-based wa-termarking, the detection could be guaranteed to be error-freein the absence of noise even when the host signal is unavailable,but not in the SS watermarking. The correlation-base detection,which is the most common method of extracting the messageembedded by SS watermarking, has the weakness of combatingthe interference from the host signal.

As discussed in Section I, let the watermarked signal be de-noted by and the attacked watermarked signal bedenoted by . If the components of the spreading vector

are randomly drawn from , the embedding-induceddistortion is

(18)

where denotes the dimension of the spreading vector, andhence the capacity of embedding is bits per sample.Regarding the robustness analysis, the probability of detectionerror, under zero-mean Gaussian noise attack, is given by [9]

(19)

where and represent the variances of the host signal andnoise, respectively. Moreover, the DNR is defined as in (8).Equation (19) is determined by the assumption that the hostsignal is Gaussian distributed with zero mean, and is unavail-able at the receiver end. If the extracting involves the host signal(informed detection), without the host signal interference, theprobability of error detection is

(20)

Though the informed detection is of limited usefulness in prac-tice, (20) can provide a goal which the watermarking schemeswith blind detection pursue.

To alleviate the interference of the host signal in blind detec-tion, Malvar et al. [9] proposed the ISS which modulates theenergy of the inserted watermark to compensate for the host-in-terference. A simpler version of the ISS is

(21)

In [9], the authors proposed a method of tuning the parametersand so as to cause the same degree of distortion as SS and

minimize the probability of detection error. Thus, the bit-errorrate is given by

(22)

where

(23)

D. Robustness Improvement of the Previous Works

This investigation presents and discusses the improvements inrobustness achieved by previous works. As the applicable con-dition adopted in Section II-B, the PSNR of the watermarkedand the attacked watermarked images are set to 40 and 35 dB,respectively. Fig. 5 shows the probabilities of error detection fordifferent ranges of . The number of bits that can be embeddedinto the host image decreases with increasing . Besides, in theSS-based watermarking, the is set to be 45.5

Fig. 5(a) clearly illustrates that the ISS approach indeed im-proves the robustness in the SS approach, especially in casesinvolving low capacity. However, the ISS approach can onlyoutperform the quantization-based watermarking in cases in-volving very low capacity, as shown in Fig. 5(b). Notably, the10-based logarithms of the low probabilities are presented todemonstrate their performances clearly. However, few bits canbe embedded into an image in such low-capacity cases. For ex-ample, only 64 bits of a message can be embedded into an imageof 256 256 for .

Regarding the LUT approach, Fig. 5(c) shows that it haslower error rate than the conventional quantization-basedwatermarking in high-capacity cases, which have very high

. Namely, the LUT approach is suitable for application inscenarios which do not demand high accuracy or capacity. Thefollowing section presents the proposed scheme which achievessuperior robustness to the conventional quantization-basedwatermarking in most of the applicable scenarios.

III. IMPROVED QUANTIZATION-BASED WATERMARKING

For the conventional quantization-based watermarking illus-trated in Fig. 2, the watermark message is embedded by mod-ifying the host value to the quantized value or , whichis the center of the objective interval. Choosing the center asthe quantized value is inherited from the quantization approachapplied to compression or coding in order to minimize the quan-tization error. The rationale for the proposed scheme is that thewatermarking does not demand a minimal and limited numberof quantized values to lower the number of bits required for

5From (19), � influences the P in spread spectrum watermarking. There-fore, the value of 45 is chosen for mimicking the host image is “Lena” which isa common test image.



Fig. 5. Comparison of various approaches. (a) L = 1 � 255. (b) L = 256 �

2048. (c) L = 1 � 16.

storage or transmission in compression or coding. Accordingly,the quantized values should not be fixed at the centers of the in-tervals, but rather should be determined flexibly with reference

Fig. 6. Quantized values are determined according to the embedded messageand the host feature x.

to the host value and considering the embedding-induced dis-tortion and robustness.

As shown in Fig. 6, let the host feature , ,and the quantized values , , and

, , selected according to the messagesand , respectively. The embedding-induced distortionwill be

(24)

if the distribution of the binary watermark message is equallyprobable.

Like (6), for the symmetrical and unimodal noise , the prob-ability of detection error will be approximately

(25)

Fig. 7(a) and (b) reveals that the two-dimensional contourplots of and , respectively, where the noise is assumedto be Gaussian. In Fig. 7(a), the host value is , for quanti-zation step of 3, while in Fig. 7(b), the error-rate is found by(25) regardless of the host value. Clearly, the distortion anderror rate assume radiation shape increasing from

and , respectively. Observing thesetwo plots, modifying the host value to the points inan iso-distorted line in Fig. 7(a) has different probabilities oferror detection in Fig. 7(b); and modifying the host value to thepoints in an iso-erroneous line in Fig. 7(b) also inducesdifferent extents of distortion in Fig. 7(a). Thus, multiple pos-sible quantized values exist for a tolerable distortionlimit, and the value which causes the minimum error probabilityshould be selected. Furthermore, for the fixed DNR, Fig. 8(a)and (b) shows that the best determination of dependson the host value , rather than being constantly fixed at(0,1).

Fig. 9 illustrates how to determine and for a given con-straint on embedding-induced distortion, where Fig. 9(a) and(b) is shown for and , respectively. From (24), allof the points on the dash-circles centered at in



Fig. 7. Embedding-induced distortion and the error probability of detection fordifferent � and � . (a) D, for q = 3 and � = 0:3. (b) P , for q=� = 5.

Fig. 9(a) and (b) induce the same extent of distortion. Moreover,the distortion increases with increasing distance from .However, only the points in the gray zone are valid candidatesfor quantized values. Notably, in Fig. 7(b), the error rates ra-dially increase from the for . Conse-quently, within the range of the tolerable distortion limit, thequantized values should be as close to (0,1) as pos-sible; and should be as close to (0, 1) as possible when

. Based on the above observation, for ,is proposed to be the intersection of the circle constraining the

Fig. 8. Probability of error detection for different � and � for DNR of 3 dB.(a) � = 0:3. (b) � = 0:4.

distortion and the line between and (0,1). That is, the fol-lowing equations are solved:

(26)

where denotes the radius of the circle in Fig. 9(a)

(27)



Fig. 9. Determining � and � for (a) 0 < � < 1=2 and (b) �(1=2) < � <0. (Only the points in the gray zone are valid candidates for quantized values.)

and is determined by the tolerable embedding distortion andquantization step . Since ranges from 0 to 1/2, should bein the range

(28)

so that a valid in the gray zone can be found. Accord-ingly, the quantization step is set in the following range:

(29)

The solution of (26) for and , isgiven by

(30)

Similarly, for , solving the following equations:

(31)

results in:

(32)

Consequently, given a tolerable distortion , the quantizationstep can be determined flexibly using (29), and the quantizedvalues can be analytically determined in a closed-form solutionaccording to the host value and the message to be embedded by(30) and (32), respectively.

Additionally, since the quantized values are always at the cen-ters of the quantization intervals in the conventional quantiza-tion-based watermarking schemes, the watermarked value canbe regarded as the data drawn from a finite set which consists ofthe points separating a multiple of quantization step from others.Thus, the quantization step is easily inferred. However, the pos-sible values of the watermarked data of the proposed scheme areno longer finite, creating a barrier to the disclosure of the quan-tization step.

IV. EXPERIMENTAL RESULTS

A. Gaussian Distributed Host Signal

In this subsection, the host signal comprises 1 000 000samples drawn from the pseudo-random Gaussian distribution

, and the watermark message is also randomly gen-erated with , where eachsample of the host signal conveys one bit of the watermarkmessage. The watermarked signal is subjected to attacks whichsuperimpose Gaussian noise on the watermarkedsignal to the extent that the DNR ranges from 10 to 5 dB.

In Fig. 10, all of the quantization steps are adjusted to theextent that the embedding-induced distortion is 6. This set-ting somewhat resembles the case in which the host image is an8-bit gray-level image and the PSNR of the watermarked imageis 40 dB. From [9], the performance of informed-SS could bepresented as a bound for comparison. Obviously, the proposedscheme has a lower error rate than the conventional quantiza-tion watermarking scheme and the LUT approach in scenarioswhere the DNR ranges from 10 to 5 dB. The proposed schemeimproves the robustness and approaches the bound more closelythan other quantization-based watermarking schemes. If theDNR is set to 0 dB, the proposed scheme, compared to theconventional quantization watermarking, could even reduce theerror probability by 0.113, whereas the reduction is only 0.037for the LUT approach. Especially, the proposed scheme canoutperform the conventional approach in cases where the LUTapproach cannot.



Fig. 10. Probability of error detection for the Gaussian distributed host signal.

Fig. 11. Host and the watermark images: (a) Host image (256 � 256).(b) Watermark image (64 � 64). (c) Scrambled image of (b). (d) Watermarkimage (128 � 128). (e) Scrambled image of (d).

B. Embedding Bilevel Watermark Into Gray-Level Image

In this subsection, the host signal comes from a 256256 gray-level image, shown in Fig. 11(a). As discussed inSection II-B, the capacity can be traded for reducing the embed-ding-induced distortion. Therefore, the host image is dividedblock-wise and each of the blocks forms a vector . Everyvector conveys one bit of the watermark message. Fig. 11(b)and (d) shows the bilevel watermark images of 64 64 and128 128 for the embedding capacities of 1/16 and 1/4 bitsper sample, respectively. As discussed in Section I, both of thewatermark images are scrambled to resist the cropping attack,and the and are equalized, as shown inFig. 11(c) and (e). The embedding is conducted by quantizingthe projection value of the host vector along a random direction.To let the embedding be unnoticed, the quantization step is

Fig. 12. Watermarked images for (a) L = 16 and (b) L = 4. (PSNR =40 dB).

Fig. 13. Watermarked image (L = 16) is subject to the Gaussian noise attacksuch that the PSNR is (a) 25 dB, (b) 30 dB, (c) 35 dB, and (d) 38 dB, respectively.(e)–(h) Extracted watermark images of (a)–(d), respectively.

adjusted to the extent that the PSNR of the watermarked imageis 40 dB. Fig. 12(a) and (b) shows the watermarked images ofthe proposed scheme for and 4, respectively.

The robustness test is first conducted by superimposing theGaussian noise on the watermarked image,where is set to the extent that the PSNR of attacked wa-termarked image ranges from 25 to 38 dB. Figs. 13 and 14show the attacked watermark and the extracted watermarkimages. Obviously, provided the noise does not deterioratethe watermarked image too much, the extracted watermarkimage is clearly discernible. The difficulty in recognizing the



Fig. 14. Watermarked image (L = 4) is subject to the Gaussian noise attacksuch that the PSNR is (a) 25 dB, (b) 30 dB, (c) 35 dB, and (d) 38 dB, respectively.(e)–(h) Extracted watermark images of (a)–(d), respectively.

extracted watermark image reduces with decreasing distortionimposed on the watermarked image. Observing and comparingFigs. 13 and 14 can clarify the influence of on robustness.The extracted watermark is still faintly visible when the wa-termarked image deteriorats to dB in the case of

. However, in the same scenario for , the extractedwatermark image just appears to be a random pattern. Fig. 15(a)and (b) compares the robustness of the proposed scheme withthat of other quantization-based watermarking schemes whenthe watermarked image is subjected to Gaussian noise attack.As in Section IV-A, the proposed scheme outperforms the othertwo quantization-based watermarking schemes.

The following compares the robustness of the proposedscheme and other quantization-based watermarking schemesunder nonGaussian noise attack. Here, different levels of JPEGcompression are applied to the watermarked image, becausethe JPEG standard is a common method of compressing thestill images. Fig. 16 shows the error probabilities of the ex-tracted watermark. The proposed scheme still outperforms theconventional quantization-based watermarking scheme whenthe watermarked image is subject to a high compression; andalways outperforms the LUT approach.

In Figs. 15 and 16, the compared approaches are all blind wa-termarking methods except for the informed-SS of which per-formance, as aforementioned, was presented as the bound [9].As regards the blind-SS, it inevitably suffers the interferencefrom the host signal, which seriously degrades the robustness

Fig. 15. Probability of error detection where the watermarked image is sub-jected to Gaussian noise attack. The PSNR of the watermarked image is 40 dB.(a) L = 16. (b) L = 4.

Fig. 16. Error probability of detection where the watermarked image is sub-jected to JPEG compression. The PSNR of the watermarked image is 40 dB.

performance as shown in Fig. 5, and thereby be excluded inthose comparisons.



V. CONCLUSION

Based on the quantization approaches applied in compressionor coding, the quantization-based watermarking schemes gen-erally quantize the host value to the center of the quantizationinterval. However, this inheritance only considers the ability toresist attack, and hence the control of quantization error (theembedding-induced distortion in watermarking) resorts to ad-justing the size of the quantization interval. This work presentsthat this is not necessarily true, yet the quantized value shouldbe flexibly determined by the host value. Given tolerable em-bedding-induced distortion and the watermark message to beembedded, this work proposes a method of analytically deter-mining the quantized value, and thus reaches a compromise be-tween robustness requirements and the transparency of the wa-termarking scheme.

The simulation results demonstrate that the proposed schemeoutperforms the other quantization-based watermarkingschemes. In the scenario of inducing the same degree of distor-tion, the proposed scheme always has lower probability of errordetection than the other schemes. Additionally, the proposedscheme has better nondisclosure of the quantization step owingto the difficulty of inferring the quantization step from thewatermarked data.

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Soo-Chang Pei (SM’89–F’00) was born in Soo-Auo,Taiwan, R.O.C., in 1949. He received B.S.E.E. de-gree from National Taiwan University, Taipei,Taiwan, R.O.C., in 1970 and M.S.E.E. and Ph.D.degrees from the University of California, SantaBarbara, in 1972 and 1975, respectively.

From 1970 to 1971, he was an engineering officerin the Chinese Navy Shipyard. From 1971 to 1975,he was a Research Assistant at the University ofCalifornia, Santa Barbara. He was the Professor andChairman in the Electrical Engineering department

of Tatung Institute of Technology and National Taiwan University from 1981to 1983 and 1995 to 1998, respectively. Presently, he is the Dean of ElectricalEngineering and Computer Science College and the Professor of ElectricalEngineering department at National Taiwan University. His research interestsinclude digital signal processing, image processing, optical information pro-cessing, and laser holography.

Dr. Pei received the National Sun Yet-Sen Academic Achievement Award inEngineering in 1984, the Distinguished Research Award from the National Sci-ence Council from 1990 to 1998, the Outstanding Electrical Engineering Pro-fessor Award from the Chinese Institute of Electrical Engineering in 1998, theAcademic Achievement Award in Engineering from the Ministry of Educationin 1998, the Pan Wen-Yuan Distinguished Research Award in 2002, and the Na-tional Chair Professor Award from Ministry of Education in 2002. He has beenPresident of the Chinese Image Processing and Pattern Recognition Society inTaiwan from 1996 to 1998, and is a member of Eta Kappa Nu and the OpticalSociety of America (OSA). He became an IEEE Fellow in 2000 for contribu-tions to the development of digital eigenfilter design, color image coding andsignal compression, and to electrical engineering education in Taiwan.

Jun-Horng Chen (S’02–M’05) was born in Yu-Lin,Taiwan, R.O.C., in 1966. He received the B.S. degreein electronic engineering from National Taiwan Uni-versity of Science and Technology, Taiwan, R.O.C.,in 1991, and the M.S. and Ph.D. degrees in electricalengineering from National Taiwan University,Taiwai, R.O.C., in 1993 and 2005, respectively.

He is currently an Associate Professor and theChairman of the Communication Engineering De-partment, Oriental Institute of Technology, Taipei,Taiwan, R.O.C. His research interests include digital

image processing and wireless communication.


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